Amp or DAC?

I have a pair of Audio Technica ATH-A900s (Audio-Technica - Products - Other - Discontinued - ATH-A900), that have a 40ohm impedance. I use them quite a lot for early morning TV viewing from a Sky box and a new Xbox One, both of which have optical outputs. Currently they are running into an old Pioneer receiver which has 2 optical in's that I can switch between, but I'm not sure the headphone socket on that receiver is a decent signal for my cans - the sound doesn't seem to reflect the quality of the phones. Regardless though, its a massive overkill for what I need!

So I'm looking for a small unit to sit under the TV, ideally USB powered (in use, and not just for charging), and take an optical signal, and give me a decent headphone amplification too. (I don't mind if I only have 1 optical input, as eventually the Sky box will run through the Xbox One, so I'll only need the one).

I'm slightly confused about the DAC side of things - I'm assuming I do need one, since the optical is a digital signal? I'd really appreciate some suggestions for suitable units around the 100 quid mark.

If you want to plug your headphones directly into the unit then you will need an amp/dac combo. For £100 you can get the FiiO E17 - It's a portable amp/dac that is USB powered. It will be perfect for what you want and you can also use it with portabe devices such as music players, phones and computers.